I found this recipe for egg free sponge cake from the vahrehvah.com cooking site. It uses condensed milk and icing sugar (they call it powdered sugar) along with coca-cola to give the necessary lift and binding that is missing when you remove eggs from a sponge recipe.
It works really well. The cooking times are pretty aggressive and I bottled out and left it in for 25 minutes instead of 15, which was a mistake. Go with the timings they give you.
The full text of the recipe is available on the vahrehvah website.
I made this chocolate icing which was extra yummy.
Copacetic 